GATE CS 2022 Q.5: Spatial Aptitude

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.

Two square letter plates showing upright capital letters A and D.

From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.

Three square letter plates: upright D, horizontally mirrored D, and upright J.

Three square letter plates: upright R, 180-degree rotated A, and 180-degree rotated R.

Three square letter plates: upright Z, 180-degree rotated E, and upright D.

Three square letter plates: upright I, 180-degree rotated L, and upright Y.

Official answer and solution

Official answer: B
From: Official GATE 2022 answer key

Solution

Determine the necessary letter frequencies for a 5-letter palindrome and find the matching combination of plates.

A 5-letter palindrome has the symmetric structure $L_1 L_2 L_3 L_2 L_1$ . This requires exactly one central letter of odd frequency (occurring 1 time) and two pairs of matching letters (each occurring 2 times).

The two given plates contain the letters 'A' and 'D'. The letter 'D' appears once and has no partner, so 'D' must be the central letter ( $L_3 = \text{'D'}$ ).

To complete the palindrome, we already have one 'A', so we need another 'A' to form the pair $\{L_2, L_4\}$ . The remaining pair $\{L_1, L_5\}$ must consist of two identical letters.

Option (B) provides plates with letters 'R', 'A', 'R'. Together with the given plates 'A' and 'D', we have the letters $\{\text{'R'}, \text{'R'}, \text{'A'}, \text{'A'}, \text{'D'}\}$ , which form the 5-letter palindrome 'RADAR'.

Final answer

Option (B)

Common trap

Overlooking that a 5-letter palindrome requires two distinct matching pairs and one single central letter.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2022 Computer Science and Information Technology (CS)
Question: 5 of 65
Section: General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source